How to calculate the phase margin from Bode Plot if only the phase angle corresponds to the pole frequencies are given?

Question

I have a Bode plot where only the phase angle corresponds to the two pole frequencies are given. The value of gain crossover frequency where the loop gain is unity is unknown.

$$\mathrm{PM} = \phi - (-180^{\circ})$$

I know PM can be calculated by checking the usual formula as above, but what could be the other criteria for performing this solution? Is the phase margin going to 180 degrees for this two pole (I assume it is 2 pole system as only two poles are given, you can correct me if I am wrong here)? Or, is it going to be (180+(-90-45-135) = -90? The transfer function could be

$$H(s) = \frac{1}{(s+\omega_{p1})(s+\omega_{p2})}$$

Answer 1

How to calculate the phase margin from Bode Plot if only the phase angle corresponds to the pole frequencies are given?

Use asymptotes for -90 deg per 2 decades per pole ( +90 per zero), centred on the breakpoint, thus 45 deg at the breakpoint.

This is just as you would draw -20 dB per decade per pole and +20 dB/zero) . Just as the gain deviates 3.01 dB from the asymptotic straight line with a curve at the breakpoint, the phase deviates 5.3 degrees at +/-1 frequency decade from the 0 and 90 deg change in angle.

Now you can quickly draw the values on a log Av vs log f scale.